Two astronauts on opposite ends of a spaceship are comparing lunches. One has ap

Question

Two astronauts on opposite ends of a spaceship are comparing lunches. One has apple, the other has an orange. They decide to trade. Astronaut 1 tosses the 0.128 kg apple toward astronaut 2 with a speed of 1.15 m/s. The 0.163 kg orange is tossed from astronaut 2 to astronaut 1 with a speed of 1.23 m/s. Unfortunately, fruits collide, sending the orange off with a speed 1.13 m/s and an angle of 41.0 degree with respect to its original direction of motion. Using conservation of linear momentum, find the final speed and direction of the apple. Assume an elastic collision. Give the apple's direction relative to its original direction of motion. Please show detailed calculations.

Explanation / Answer

from conservation of,m omentum

m1u1x+m2u2x = m1v1x+m2v2x

0.128*1.15-0.163*1.23 = 0.128*v1x+0.163*1.13cos41

0.147-0.2-0.139 = 0.128v1x

v1x = -1.5 m/s

along y axis

0 = m1v1y-0.163*1.13sin41

v1y = 0.944 m/s

v1 = sqrt(v1x^2+v1y^2) = 1.77 m/s

theta = tan^-1(v1y/v1x) = 32.18 degrees

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